The Federal Reserve had set a 6.5 percent unemployment rate as its marker for when to consider raising interest rates, which the bank relays to the market through forward guidance. CNBC's March Fed Survey showed that 95 percent of central bank observers expect Yellen to move away from the unemployment threshold.

The unemployment rate sunk to 6.7 percent in the past few months amid patchy economic data from a frigid, industry-slowing winter. That led Fed watchers to call into the question tying interest rates to a hard-and-fast threshold.

Rivlin said a 6.5 percent rate can paint a misleading picture on job growth, giving the impression that labor markets are strong when other factors suggest otherwise. Tethering policy to 2-percent inflation remains fine, but the Fed uses many other employment indicators than just the unemployment rate, Rivlin said.

"Plenty of Fed people including Chair Yellen have said they don't just look at the unemployment rate," Rivlin said.

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The big question on Wall Street is over when the Fed will begin to raise interest rates now that the central bank has steadied its plan to reduce its bond purchases by $10 billion a month, said Chad Morganlander, a portfolio manager at Stifel Nicolaus.

With inflation staying low, Morganlander doesn't see the Fed raising interest rates until late 2015 or even 2016.

Kenneth Rogoff, a professor of economics and public policy at Harvard University, told CNBC that Yellen's biggest test lies in how the Fed communicates with the markets, especially since he expects inflation to pick up.

"That's the big concern as she gives her first press conference," Rogoff said. "How does she assuage markets, how does she assure them that she intends to stay the course ... so that interest rates don't go up ahead of what she wants?"

—By CNBC's Jeff Morganteen. Follow him on Twitter at @jmorganteen and get the latest stories from "Squawk on the Street."